Deterministic broadcasting in unknown radio networks

We consider the problem of distributed deterministic broadcasting in radio networks of unknown topology and size. The network is synchronous. If a node u can be reached from two nodes which send messages in the same round, none of the messages is received by u. Such messages block each other and node u either hears the noise of interference of messages, enabling it to detect a collision, or does not hear anything at all, depending on the model. We assume that nodes are completely ignorant of the network: they know neither its topology, nor size, nor even their immediate neighborhood. The initial knowledge of every node is limited to its own label. We study the time of deterministic broadcasting under this total ignorance scenario. Previous research has concentrated on distributed randomized broadcasting algorithms working for unknown networks, and on deterministic off-line broadcasting algorithms assuming full knowledge of the radio network. Ours are the first broadcasting algorithms simultaneously distributed and deterministic, that work for arbitrary totally unknown radio networks. The results for the model without collision detection: We develop a linear-time broadcasting algorithm for symmetric graphs, which is optimal. For arbitrary n-node graphs, we prove a lower bound Ω(D log n), where D is the diameter, and develop an algorithm working in time O(n^11/6). Next we show that broadcasting with acknowledgement is not possible in this model at all. For the model with collision detection, we develop efficient algorithms for broadcasting and for acknowledged broadcasting in strongly connected graphs.